First-half goals from Nicolas Otamendi and Sergio Aguero underlined the Blues dominance, and skipper Aguero added a third after the break.
The Saints pulled a late consolation back, but the holders’ passage to the last eight was never in any real doubt.
The defending champions started in determined fashion against a wounded Southampton side, still reeling from last Friday’s 9-0 home loss to Leicester City.
Fielding teenagers Tommy Doyle, Eric Garcia and Phil Foden, Pep Guardiola selected a side that had a mixture of youth and experience, with Bernardo Silva as creator-in-chief in central midfield and Gabriel Jesus on the left flank.
Claudio Bravo had barely had a touch by the time the hosts took the lead as Otamendi headed home Bernardo’s cross from the left on 20 minutes.
Saints offered little in the way of response, perhaps looking to avoid another pummelling as much as anything else, so when City doubled the lead just before the break, it was no real surprise.
A sweeping move that began in defence, ended with Riyad Mahrez feeding the overlapping Kyle Walker and his low cross was volleyed home by Aguero on his 350th appearance for the Club.
And it was Aguero who put the game to bed on 57 minutes with his second of the night and his twelfth of the campaign.
Bernardo cut in from the right before finding Mahrez who then hit a deflected cross towards goal and Aguero expertly guided the ball past Alex McCarthy to make it 3-0.
It wasn’t until the 65th minute that Bravo was called into action, but the inactivity hadn’t dulled his reflexes as he made a fine fingertip save from Sofiane Boufal.
Jack Stephens headed a consolation goal for the Saints on 76 minutes, but it was too little, too late for the visitors.
Doyle impresses on debut
It was a proud night for the Doyle family as Tommy made his senior bow.
The 18-year-old midfielder was given the anchor role in front of the back four and rarely put a foot wrong.
And it’s not hard to guess how he must have felt as he ran out to see a huge flag of his granddad Mike Doyle in the South Stand.
If he needed any extra inspiration, the thought of how proud the granddad he lost would surely have been at the forefront of his mind.
Star man: Sergio Aguero
Two more for the Club’s record goal-scorer on his 350th appearance for City.
“Eric Garcia has once again played a high level, like has this season and last season in the Carabao,.
“He didn’t make one mistake. Tommy Doyle, as well, he played well in position that isn’t his natural his position.
“I thought he played really well. Congratulations on his debut. I’m so sorry for Ian Carlo Poveda who was about to come on - but at 3-1 the game wasn’t over and after Angelino’s injury, John Stones had to play.
“We have Fernandinho who can play as holding midfielder but he is playing centre-back (and was suspended tonight).
“That’s why Tommy played. I didn’t have another alternative. He was with us in pre-season and I’ve seen him in the Academy. I didn’t have any doubts he would play a good level."
What it means….
City go into the Carabao Cup quarter-finals with the draw to be made this Thursday morning (8.45am GMT) on BBC Radio 2.
It’s as you were for the Blues who again entertain Southampton, this time in the Premier League – kick-off 3pm, Saturday 2 November.